linear programming problem

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QUE 1

Consider the following .

The tableau corresponds with a step of the SIMPLEX
method applied to the previous problem.

  1. What is the value of the variables  and the objective function?
  • Identify the entering and
    the leaving variables. Justify your response with the calculations performed
    (you can extend the previous tableau to perform the required calculations)
Entering Variable:
 
Leaving Variable:
  • Based
    on the information summarized in the sensitivity report of Excel (corresponding
    to the optimal solution, answer the following questions.
  1. How it affected the value
    of objective function if the right side of the third constraint increase in 2
    units? Justify
    with the calculations performed
  • How many units is possible
    to increase the right side of the third constraint without losing the geometry
    of the current optimal solution

Que 2.

The ABC
Company is planning to replace its current electrical infrastructure with a new
special system. Since the new system has more capacity it is not necessary to
maintain all the current connections. The manager wishes to decide which pairs
of offices should be directly connected in order to ensure that every office is
connected (directly or indirectly) in the new system. The figure shows the
current infrastructure: the letters represent the offices and the arcs, the
connections. The numbers represent the distances between the corresponding
nodes.

 In order to minimize the cost: What are the
offices that must be directly connected? Assuming that for the new system is
required 3 units of cable for each unit of distance, how many units of cable
should be purchased by the company? Justify with the calculations performed.

  1. Is this problem P or NP? Justify

Que 3.

The town hall of a city wants to open some
recreational centers. It has been analyzed 3 options. The opening cost and the
capacity of each center are listed below.

The
selected recreational centers must be hosting the students from 5 schools. In
the table below is summarized the number of students at each school.

Each
school must be assigned to only one recreational center. And the capacity of
each center must be respected. What are the recreational centers that must be
open in order to minimize the opening cost?

  1. Formulated a mathematical programming model. (Linear
    Model is required)
  2. Modify the previous model such that are considered the
    following constraints:
  3. One school can be assigned to several recreation
    centers
  4. It is decided to open at most two recreation-center
  5. Design a greedy solution strategy for the problem
    described in 1.
  6. Illustrate the greedy procedure with the following
    data:

Que 4.

Answer the
following questions:

  1. What is a
    flow-oriented simulation software (such as FlexSim) used for? 
  2. Explain why simulation software’s are
    used?

Answer the
following questions related to FlexSim software:

  • The main resources found in any simulation
    model are source, queue, processor and sink. Briefly explain the role of each.
  • Which kind of connection may be used to
    connect the above-mentioned resources?
  • What does the “machine
    throughput” measure?

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